There are various VGA adapters out there. I got a custom one off ebay for $40. You have to remember that some Gamecube games don't support 480p resolution so they won't even work on VGA.
This right here will do the trick and shouldn't break the bank. I already have one and it works great. Just make sure you have a GC video cable that has S-Video on it. If you don't have one already, shell out a couple bucks and get one - because with composite it will look like crap if you're not using a TV since monitors are high-def.